A search for time-dependent violation of the charge-parity symmetry in $D^0 \to K^+ K^-$ and $D^0 \to \pi^+ \pi^-$ decays is performed at the LHCb experiment using proton-proton collision data recorded from 2015 to 2018 at a centre-of-mass energy of 13 TeV, corresponding to an integrated luminosity of 6 fb$^{-1}$. The $D^0$ meson is required to originate from a $D^*(2010)^+ \to D^0 \pi^+$ decay, such that its flavour at production is identified by the charge of the accompanying pion. The slope of the time-dependent asymmetry of the decay rates of $D^0$ and $\bar{D}^0$ mesons into the final states under consideration is measured to be $\Delta Y_{K^+ K^-} = (-2.3 \pm 1.5 \pm 0.3) \times 10^{-4}$, $\Delta Y_{\pi^+ \pi^-} = (-4.0 \pm 2.8 \pm 0.4)\times 10^{-4}$, where the first uncertainties are statistical and the second are systematic. These results are compatible with the conservation of the charge-parity symmetry at the level of 2 standard deviations and improve the precision by nearly a factor of two.
Requirement of the single-track selection of the first-stage software trigger in the $\chi^2_{\text{IP}}$ vs. $ p_{\mathrm{T}}$ plane, for the three configurations employed during data taking. The dashed region is excluded by the loosest configuration. |
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Distribution of $ m( D ^0 \pi ^{+}_{\mathrm{ \scriptscriptstyle tag}} )$ for (top) $ D ^0 \rightarrow K ^- \pi ^+ $ , (left) $ D ^0 \rightarrow K ^+ K ^- $ and (right) $ D ^0 \rightarrow \pi ^+ \pi ^- $ candidates. The signal window and the lateral window employed to remove the combinatorial background (grey filled area) are delimited by the vertical dashed lines. Fit projections are overlaid. |
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Distribution of $ m( h ^+ h ^- )$ for (top) $ D ^0 \rightarrow K ^- \pi ^+ $ , (left) $ D ^0 \rightarrow K ^+ K ^- $ and (right) $ D ^0 \rightarrow \pi ^+ \pi ^- $ background-subtracted candidates. The signal window is delimited by the vertical dashed lines. |
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(Left) sum and (right) asymmetry of the distributions of the momentum of $\pi ^{+}_{\mathrm{ \scriptscriptstyle tag}}$ and $\pi ^{-}_{\mathrm{ \scriptscriptstyle tag}}$ candidates, projected on the (top) $k$ vs. $\theta_x$ and (bottom) $\theta_y$ vs. $\theta_x$ planes, for the $ D ^0 \rightarrow K ^- \pi ^+ $ candidates collected in 2017 with the Mag Up polarity. The angles $\theta_{x(y)}$ and the curvature $k$ are defined in the text. The asymmetries during the other data-taking years are similar, and opposite in sign for the data collected with the MagDown polarity. The regions of the distributions with asymmetries whose magnitude is larger than 20% are plotted with the same colour as $\pm 20\%$. These regions are discarded from the data sample after the kinematic weighting. |
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(Top) Normalised distributions of the $ D ^0$ transverse momentum, in different colours for each decay-time interval. Decay time increases from blue to yellow colour. (Centre) Asymmetry between the normalised $ p_{\mathrm{T}} $ distributions of $ D ^0$ and $\overline{ D } {}^0$ mesons. (Bottom) Linear fit to the time-dependent asymmetry (red) before and (black) after the kinematic weighting. All plots correspond to $ D ^0 \rightarrow K ^- \pi ^+ $ candidates recorded with the Mag Up polarity in (left) 2016 and (right) 2017. |
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Results of the fits to the time-dependent asymmetry for each subsample, for (top) $ K ^- \pi ^+ $ , (bottom left) $ K ^+ K ^- $ and (bottom right) $\pi ^+ \pi ^- $ final states. In the $y$-axis labels, the data-taking year is abbreviated with the last two digits only and the magnet polarity Mag Up ( MagDown ) is abbreviated as "Up" ("Dw"), while "Avg." denotes the weighted average. The fit $\chi^2/\mathrm{ndf}$ are reported on the right of each plot. Empty red squares and solid black dots correspond to data before and after the equalisation of the $\pi ^{+}_{\mathrm{ \scriptscriptstyle tag}}$ and $ D ^0$ kinematics, respectively, and prior to subtracting the contribution of secondary decays described in Sect. 6. |
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Impact parameter distribution of the $ D ^0 \rightarrow K ^- \pi ^+ $ candidates for the (top) first, (left) middle and (right) last decay-time interval. The projections of the two-dimensional template fit are superimposed. |
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(Left) Fraction of secondary decays from $ B $ mesons measured in the template fit. Only statistical uncertainties are displayed. (Right) Measured asymmetry, after the kinematic weighting, of data with $\mathrm{IP}( D ^0 ) > 100 \upmu\text{m} $ in the enlarged $ m( D ^0 \pi ^{+}_{\mathrm{ \scriptscriptstyle tag}} )$ signal window. The fit of a constant function is shown in red, while the $1\sigma$ band corresponding to the possible impact of $ B ^0$ mixing is plotted in cyan. |
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Asymmetry, $A_\mathrm{sig}(t)$, of $ D ^0 \rightarrow K ^- \pi ^+ $ candidates as a function of decay time. A linear fit is superimposed. The $\chi^2/\mathrm{ndf}$ of the fit is $17/19$. |
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Relative shift of the $ D ^{*+}$ and $ D ^{*-}$ mass peaks as a function of decay time for the $ K ^- \pi ^+ $ decay channel. |
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Distributions of $ m( h ^+ h ^- )$ of (top) $ K ^- \pi ^+ $ , (left) $ K ^+ K ^- $ and (right) $\pi ^+ \pi ^- $ final states, with the results superimposed. The background components are stacked; the $ m( h ^+ h ^- )$ template PDF of the $ D ^+_ s \rightarrow K ^+ K ^- \pi ^+ $ decay has a negative contribution to the left of the known $ D ^0$ mass due to the subtraction of the $ m( D ^0 \pi ^{+}_{\mathrm{ \scriptscriptstyle tag}} )$ background. The vertical dashed lines delimit the signal region. |
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Asymmetry, $A_\mathrm{sig}(t)$, as a function of decay time for (top) $ D ^0 \rightarrow K ^+ K ^- $ and (bottom) $ D ^0 \rightarrow \pi ^+ \pi ^- $ candidates. A linear fit is superimposed. The $\chi^2/\mathrm{ndf}$ of the fits are $15/19$ and $21/19$, respectively. |
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Animated gif made out of all figures. |
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Summary of the systematic uncertainties, in units of $10^{-4}$. The statistical uncertainties are reported for comparison. |
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Created on 27 April 2024.